An Evaluation of Economic Efficiency of Finnish Regions by Dea and Tobit Models* **
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AN EVALUATION OF ECONOMIC EFFICIENCY OF FINNISH REGIONS BY DEA AND TOBIT MODELS* ** Heikki A. Loikkanen Department of Economics FIN-00014 University of Helsinki, Finland [email protected] Ilkka Susiluoto Department of Economics FIN-00014 University of Helsinki, Finland [email protected] Abstract: In the first phase of the study, private sector economic efficiency scores for 83 Finnish regions in 1988-1999 were estimated by the Data Envelopment Analysis (DEA) method. Inputs in the DEA analysis included capital stock, employment by education level, years of schooling and volume of local public sector activity. Outputs were regional value added and personal direct real income from employment. Efficiency differences between regions proved to be considerable and they were correlated with several regional factors. In the second phase the differences in the efficiency scores were explained by using Tobit and logistic regression models. In these cross-section models (1988, 1993, 1999 and average of 1988-1999) the explanatory variables included regional characteristics such as population size, distance from national centres, structure of regional economy (concentration), the existence of university, number of students, accessibility index, innovativity index and the number of patents. * Paper prepared for the 42st Congress of the European Regional Science Association, Dortmund, Germany, 27. – 31.8. 2002 ** Preliminary version, not to be quoted without the permission of the authors. 1. Introduction The purpose of this paper is to present some results concerning economic performance of Finnish regions. More specifically, we study inter-regional differences in private sector efficiency (or productivity). Our data consists of regional input and output variables and other regional characteristics concerning 83 NUTS 4-level regions in Finland during the period 1988-1999. We use a two stage modelling approach. In the first stage we apply non-parametric programming techniques by using Data Envelopment Analysis (DEA). By applying DEA for each year in our study period we get annual efficiency scores for regions. Fully efficient regions get a score of one and other ones below one. In the second stage we explain (in)efficiency differences between regions with econometric methods by applying logistic regression and Tobit models. In this stage the explanatory variables are different from the DEA stage, describing the environment of productive activity (indirect inputs or externality effects), rather than direct inputs. Empirically the period 1988-99 is very exceptional in Finnish economic history. In the end of 1980s favourable international economic developments and financial deregulation lead to a boom, which was followed by a deep crisis. Unfavourable international developments, fall of exports to the former Soviet Union, domestic currency and bank crises, and pursued economic policies led to a cumulative decline of GDP of more than 10 per cent in 1991-93. Unemployment, which had been below 5 per cent in the end years of 1980s, sky rocketed to 17 per cent. From 1995 on economic growth has been exceptionally fast and the structure of the economy has changed, as IT industries have been the fastest growing sectors. Despite favourable developments unemployment has remained at high level. Also regionally recent growth has been less evenly distributed than earlier. Fewer urban areas than earlier are attracting new investment and gaining from net migration. Thus it is of interest to see whether efficiency differences obtained from DEA in early, middle and end part of the period 1988- 99 differ. On the other hand, we estimate logistic regressions and Tobit models both to explain average scores during the whole period and also study the years 1988, 1993 and 1999 separately. We want to shed light on these developments by studying regionally the relation between value added of private non-residential sector and/or taxable income, and input factors including capital stock, labour force, regional knowledge base and volume of public sector activity. This paper is organized as follows. In section 2 we describe briefly the main features of the Data Envelopment Analysis method. In section 3, data sources, as well as input and output variables are introduced. In this connection we also present the models to be employed. In section 4 we present some empirical results concerning efficiency differences across Finnish regions. In section 5 we introduce the econometric models, namely the Tobit model and logistic (log odds) regression model, which are used to explain (in)efficiency differences. Results from econometric models are presented in section 6. Section 7 offers some conclusions. 2. Data Envelopment Analysis The Data Envelopment Analysis (DEA) method of measuring (in)efficiency is fundamentally based on the work by Farrell (1957) which was further elaborated by Charnes et al. (1978) and Banker et al. (1984). This approach (see e.g. Färe et al.1985) has been widely used in empirical efficiency (or productivity) analysis especially in cases where the units (DMUs) use multiple inputs to produce multiple outputs, and there are problems in defining weights and/or specifying functional forms to be employed in analysis. As DEA does not require input or output prices in determining empirical efficiency frontiers based on best practise technology and related measures of inefficiency, it has become especially popular in the study of public sector. In the last few years several regional applications of DEA have emerged. Charnes et al. (1989) studied the economic performance of 28 China’s cities in 1983 and 1984. Chang et al. (1995) use DEA and the Malmquist productivity index approach to study the economic performance of 23 regions in Taiwan in 1983 and 1990. Tong applied DEA to investigate the changes in production efficiency of 29 Chinese provinces in two papers with somewhat different emphasis (Tong 1996, 1997). Bernard and Cantner (1997) calculate the efficiency of the 21 French provinces in 1978- 1989. In a recent study, Maudos, Pastor and Serrano (2000) analyse the relationship between efficiency and production structure in Spain 1964-93. Regional aspects are present also in several DEA studies, which concern agricultural productivity, see Weaver (1984), Mao and Koo (1997) or Millan and Aldaz (1998). To keep this paper short, we shall not present mathematically the linear programming background for DEA. We will instead graphically describe a basic case of the method. Four decision making units are described in Figure 1 below; these are the points A, B, C and D. The DMUs use one input X to produce one output Y. Either constant returns to scale (CRS) or variable returns to scale (VRS) can be assumed for the production possibility frontier. In practical research several inputs and possibly more than one output are used, creating a multidimensional situation. Under CRS, the most efficient unit is B, for which the tangent of the angle measured from the origin (output/input) is greatest (Y B / XB ). Accordingly, the efficiency frontier under CRS is the line OO. Compared with B, points A, C and D are clearly inefficient. Point D for example uses more of the input (X D ) to produce less of the output (Y D ) than point B. In order to be efficient, only X F should be used to produce YD , or alternatively YI should be produced with input use XD . From this we get XF /X D as the relative efficiency of D in the input direction; in the output direction the efficiency score is Y D /Y I . Under CRS these two ratios are equal, or (X F /X D ) = (Y D /Y I ). Under VRS the efficiency frontier passes through the points A, B and C. Consequently the relative efficiency of D is XE /X D in the input direction and YD /Y H in the output direction, these ratios being generally unequal. In VRS efficiency can be further decomposed into scale efficiency and technical efficiency. Scale efficiency relates the size of the DMU to optimal size; in the input direction it is given by the ratio (efficient input use under CRS)/(efficient input use under VRS), or X F /X E in figure 1. Similarly, scale efficiency in the output direction is Y H /Y I . This efficiency loss is due to the inoptimal size of the DMU. The rest of the inefficiency of D is technical inefficiency, measured by X E /X D in the input direction, or Y D /Y H in the output direction. Figure 1. Efficiency of decision making units in DEA, basic case Output Y O CRS Y I I C VRS Y H H Y B B F E Y D D A O X F X E X B X D Input X Finally, the change in total factor productivity of each DMU can be calculated in DEA, using the so- called Malmquist index approach. This change can be further decomposed into the change in the relative position of the DMU with respect to the efficiency frontier (PPF), and to the movement of PPF itself. For this, see Cooper, Seiford and Tone (2000). 3. Data and models in the DEA estimation of regional efficiency scores In the first phase of the study, the DEA method was used to estimate regional efficiency scores for the 83 regions for 1988-99. Real value added in the business sector was used as the main output variable. Public sector, non-profit organisations and the residential sector were excluded. Direct real income from private production was used as another output measure, consisting of wages, income from business, trade and profession, and agriculture. Pensions, income originating in the public sector and capital income were excluded. Differences in regional consumption price levels were taken into account. Consequently the figures describe real regional purchasing power of the income earned. On the input side business sector real capital stock was used as a main variable together with the number of employed.